WASHINGTON — Senator Dean Heller, Republican of Nevada, quickly found the limits of party loyalty on Tuesday when a businessman with a famous name in the state announced he was challenging him in a primary.

Mr. Heller, after weeks of publicly agonizing over Republicans’ drive to repeal the Affordable Care Act, stuck with party leadership and voted for a pared-down version of the legislation.

But Mr. Heller’s support was not enough to get the bill passed, as three other Republicans torpedoed the measure.

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On Tuesday, Danny Tarkanian, a Nevada businessman and serial candidate for elected office, announced that he would take on Mr. Heller, who was already the most vulnerable Senate Republican incumbent on the ballot next year.

Mr. Tarkanian — the son of Jerry Tarkanian, the legendary former Nevada college basketball coach — fiercely criticized Mr. Heller, calling him the personification of a wavering politician.

“He has no convictions, he doesn’t stand by his word,” Mr. Tarkanian said in an interview, citing the health care bill, federal funding for Planned Parenthood and illegal immigration.

And he said Mr. Heller would pay the price with conservative Nevada voters for refusing to back President Trump in last year’s campaign.

“I didn’t run away from the president when I ran last time when I had all sorts of pressure, so I’m certainly not going to this time when I think he’s doing lots of good things,” said Mr. Tarkanian, who narrowly lost a 2016 House race and was one of the few high-profile Nevada Republicans to not back away from Mr. Trump.

Mr. Heller, who is facing what is expected to be a well-funded opposition from Democratic Representative Jacky Rosen, greeted the news of his challenger with ridicule.

“Danny Tarkanian is a perennial candidate who has spent millions of dollars on five campaigns over the last decade,” said Tommy Ferraro, a spokesman for Mr. Heller’s campaign. “Nevada voters have rejected him every time — including less than a year ago against Jacky Rosen. He’s wasted conservatives’ time and cost the Republican Party seats up and down the ballot. If he ultimately files for U.S. Senate he will lose in the primary.”

Mr. Tarkanian declared his candidacy in an early morning interview on “Fox & Friends,” well before most Nevada voters were awake but with the assumption that Mr. Trump was tuning in from his summer vacation in New Jersey.

“We’re never going to make America great again unless we have senators in office that fully support President Trump and his ‘America First’ agenda,” said Mr. Tarkanian, the skyline of the pre-dawn Las Vegas Strip glowing behind him.

Mr. Heller has had something of a tense relationship with Mr. Trump dating back to last year’s election. It got rockier this summer after the senator and Gov. Brian Sandoval of Nevada used a heavily publicized Las Vegas news conference to excoriate a version of the Republican health care bill that would have phased out the Medicaid expansion.

A political group aligned with the White House began airing ads in Nevada criticizing Mr. Heller, only to pull them when Senator Mitch McConnell, the majority leader, and other Republican senators complained to Mr. Trump.

Yet Mr. Trump made life more difficult for Mr. Heller, the only Senate Republican running next year in a state carried by Hillary Clinton, a few weeks later in the White House.

Sitting next to the senator as cameras rolled, the president jabbed a thumb in Mr. Heller’s direction and said: “This was the one we were worried about.”

Predicting that the Nevadan would eventually fall in line, Mr. Trump offered an assessment of Mr. Heller’s political calculation that was notably short on subtlety.

“Look, he wants to remain a senator, doesn’t he?” the president said, drawing an exaggerated laugh from Mr. Heller. “And I think the people of your state, which I know very well, I think they’re going to appreciate what you hopefully will do.”

Just how much Mr. Trump appreciates Mr. Heller’s vote will play a crucial role in the primary. While conservative challengers in recent years have defeated a handful of Senate Republicans, and given even more a scare, that was before Mr. Trump took office. His decision about whether to intervene in Nevada and in Arizona, where Senator Jeff Flake is expected to face Republican opposition next year, will partly determine how much money and attention these primaries draw.

Mr. Tarkanian said he had not been in touch with the president and had not received encouragement from the White House.

Asked about what could be one of the most hard-fought primaries in the country, a senior White House official would not offer a firm declaration but did point out that Mr. Heller ultimately sided with party leaders on the health care push.

What is clear is that the senator will have both the Senate Republican campaign arm and the well-funded “super PAC” run by Mr. McConnell’s allies at his disposal.

Mr. Tarkanian argued that he would make his challenge a “national race” and gleefully noted that Fox was already replaying his interview. But he was candid when asked how he would raise enough money to muster a competitive statewide race: “I don’t know,” he said.

He invoked the example of his father, whose birthday would have been Tuesday, when pressed about his track record of losing races. He noted that the University of Nevada, Las Vegas lost year after year to more established college basketball powers before trouncing Duke in the 1990 national championship.

“Just like my dad, we’re going to persevere and we’re going to win,” he vowed.